Problem: Multiply the following complex numbers: $({-1+3i}) \cdot ({-4i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1+3i}) \cdot ({-4i}) = $ $ ({-1} \cdot {0}) + ({-1} \cdot {-4}i) + ({3}i \cdot {0}) + ({3}i \cdot {-4}i) $ Then simplify the terms: $ (0) + (4i) + (0i) + (-12 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (4 + 0)i - 12i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (4 + 0)i - (-12) $ The result is simplified: $ (0 + 12) + (4i) = 12+4i $